In this paper, we show finite time blow-up of solutions of the p−wave equation in ℝN, with critical Sobolev exponent. Our work extends a result by Galaktionov and Pohozaev [4]
This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.
We consider a special type of a one-dimensional quasilinear wave equation wtt - phi (wt / wx) wxx = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.
The semilinear differential equation (1), (2), (3), in with , (a nonlinear wave equation) is studied. In particular for , the existence is shown of a weak solution , periodic with period , non-constant with respect to , and radially symmetric in the spatial variables, that is of the form . The proof is based on a distributional interpretation for a linear equation corresponding to the given problem, on the Paley-Wiener criterion for the Laplace Transform, and on the alternative method of...